Aircraft: A321
Phase of flight: Taxi
Anomaly: ATC Issue All Types; Conflict Ground Conflict; Critical; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Ground Event / Encounter Other / Unknown; Ground Incursion Runway

FO landed Runway 35C. As we were about to exit at taxiway M2; I took over the controls. The controller issued instructions 'cross 35 left at Echo Kilo'. The FO very concisely read back 'cross 35 left Echo Kilo'. There was no response from the Tower. Normally when exiting the runway; I extinguish all but the nose taxi light. When cleared to cross a runway; I turn on all my landing; runway turn-off lights and the wing ice lights. Since we had received an immediate clearance to cross 35L; I left all the exterior lights on.As I turned the 45 or so degrees on to EK and was about ready to cross 35L; I looked out to my left to verify the runway was clear. I did not see any lights on the runway. I did see what appeared to be an RJ's lights holding short of the runway awaiting takeoff. With no response from the Tower and not seeing any red Runway Status Lights (RWSL); I proceeded across Runway 35L.As the flight deck crossed the centerline of 35L; I again looked to my left down the runway. At that point I saw an RJ; rotating and lifting off probably about 2;000 feet south of us. I had not seen his lights before and had not heard his takeoff clearance; probably because I was concentrating on our own landing and roll-out. I immediately had a bad feeling in the pit of my stomach.The ground controller gave us a phone number to call.I called the number after the aircraft was deplaned and identified myself. The Supervisor said he was trying to pull the tapes at that time and that it was 'time critical'. I gave him my number and he said he would call me back in five minutes. When I didn't receive a call in 15 minutes I called again. This time; I ended up talking to the actual controller on duty. He said the tape showed he had issued a hold short; but that the FO had read back the clearance to cross. He said he had been dealing with something on the land line and didn't hear the FO's transmission. I also mentioned the lack of a RWSL warning. He said the east side hadn't been working for a while. I mentioned that it would be nice to know this information.For my part; clarify muffled or questionable runway crossing clearances; especially at night. Brief the RWSL system; if installed or whether operational or not.The DFW airport operator and/or the FAA need to get the RWSL system up and running consistently. The more I have seen of this system in use; the more I think it could really cut down on aircraft to aircraft incursion events at busy airports. I was the flying pilot; landed Runway 35C in DFW. Rolled out; slowed down; and transferred aircraft to Captain. Exited at M2 and assumed PM duties. Captain and I both heard Tower instructing us to 'exit M2; EK cross 35L.' Read back as heard; Tower did not correct response. During the event; Tower was busy: working the runway(s); crossing traffic; and dealing with another aircraft (talking on a land line; see comment below). Runway Status Lights (RWSL) system not operating; ATIS did not broadcast system status. Cleared the runway; followed SOPs. Captain verified 'clear left;' I verified 'clear right.' Captain maintained airplane illuminated with the lights on to cross runway 35L.As we crossed; we observed an airplane lifting off; to our left; on Runway 35L. After crossing Runway 35L; contacted Ground Control. The Ground Controller told us to telephone the Tower; wrote down the phone number provided. Ground Control did not specify the reason for the call. Followed Ground Control taxi instructions. Contacted Ramp Control and followed instructions to the gate. After securing the aircraft at the gate; Captain telephoned the Tower. On the telephone conversation; Captain was notified that; during the event; the Tower Controller was talking on a land line (dealing with another aircraft) and; upon perceiving the problem; radioed us 3 times to hold short. We did not hear those radio calls. Report from two air carrier flight crews regarding a runway incursion event that resulted in an aircraft taking off with about 100 feet vertical clearance over the incursion aircraft that was taxiing across the runway.